Question: If X has an exponential distribution with the parameter
If X has an exponential distribution with the parameter θ, use the distribution function technique to find the probability density of the random variable Y = lnX.
Answer to relevant QuestionsWith reference to Exercise 7.9, find the probability distribution of the random variable Z = (X – 1)2. Exercise 7.9 If X has a hypergeometric distribution with M = 3, N = 6, and n = 2, find the probability distribution of ...Use the transformation technique to rework Exercise 7.2. In exercise If the probability density of X is given by And Y = X2 Consider the random variable X with the uniform density having α = 1 and β = 3. (a) Use the result of Example 7.2 to find the probability density of Y = | X|. (b) Find the probability density of Z = X4(=Y4). If X has the uniform density with the parameters α = 0 and β = 1, use the distribution function technique to find the probability density of the random variable Y = √X. On page 215 we indicated that the method of transformation based on Theorem 7.1 can be generalized so that it applies also to random variables that are functions of two or more random variables. So far we have used this ...
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